%I #37 Sep 08 2022 08:46:13

%S 0,29,478,4287,24476,101785,337434,946043,2333752,5206581,10714070,

%T 20633239,37597908,65378417,109216786,176222355,275832944,420346573,

%U 625528782,911300591,1302512140,1829807049,2530582538,3450050347,4642403496,6172093925,8115226054

%N a(n) = n^7 + 7*n^5 + 14*n^3 + 7*n.

%C Also numbers of the form (n-th metallic mean)^7 - 1/(n-th metallic mean)^7, see link to Wikipedia.

%H Raphael Ranna, <a href="/A261540/b261540.txt">Table of n, a(n) for n = 0..100</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Metallic_mean">Metallic mean</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = -a(-n) = ( (n+sqrt(n^2+4))/2 )^7 - 1/( (n+sqrt(n^2+4))/2 )^7.

%F G.f.: x*(29 + 246*x + 1275*x^2 + 1940*x^3 + 1275*x^4 + 246*x^5 + 29*x^6)/(1 - x)^8. - _Bruno Berselli_, Aug 24 2015

%t Table[n^7 + 7 n^5 + 14 n^3 + 7 n, {n, 0, 30}] (* _Bruno Berselli_, Aug 24 2015 *)

%t LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 29, 478, 4287, 24476, 101785, 337434, 946043}, 30] (* _Vincenzo Librandi_, Aug 24 2015 *)

%o (Sage) [n^7+7*n^5+14*n^3+7*n for n in (0..30)] # _Bruno Berselli_, Aug 24 2015

%o (Magma) [n^7 + 7*n^5 + 14*n^3 + 7*n: n in [0..30]]; // _Vincenzo Librandi_, Aug 24 2015

%o (PARI) a(n)=n^7+7*n^5+14*n^3+7*n \\ _Charles R Greathouse IV_, Aug 24 2015

%Y Cf. A001622, A014176, A098316, A098317, A098318, A176398, A176439, A176458, A176522, A261391.

%K nonn,easy

%O 0,2

%A _Raphael Ranna_, Aug 24 2015

%E Offset changed from 1 to 0 and initial 0 added by _Bruno Berselli_, Aug 25 2015